Relations and FunctionsRelation: a listed set of ordered pairs, agraph or a rule with specified or implieddomainsDomain: set of all x-valuesRange: set of all y-values
Relations and functionsFour types of relations One-to-one: one x-value to one y-value Many-to-one: more than one x-value is mapped to the same y-value One-to-many: one x-value is mapped to more than one y-value Many-to-many: more than one x-value is mapped to more than one y-value
Relations and functionsFunction: A many-to-one relation. Thegraph cannot be crossed more than onceby a vertical line drawn anywhere on thegraph.
Relations and functionsTwo types of functions: One-to-one: Graph can be crossed only once by any vertical or horizontal line Many-to-one: Graph can be crossed only once by a vertical line.The domain of many-to-one functions can berestricted to make one-to-one functions.
Relations and functionsInverse function is the reflection of aone-to-one function in the line y=xA function has an inverse function if itis a one-to-one functionThe original function and its inverseintersect on the line y=x
Relations and functionsResources Video: 283_one-to-one functions Worksheet: Functions